Does the damage keep escalating upwards? Or does it start from base value again? I'm wondering whether it's worth taking Toxic Strike just for bosses if I kill my enemies fast enough without the use of damage over time.

It will get prolonged and the ticks will increase (as if it had longer duration from the start). So yes, it will keep escalating upwards.

Keep in mind though that Toxic Strike is a poison ability and several enemies - including some bosses - are immune.